It is important that the algorithm of Corollary REF  only needs (approximate) access to distances between the \(n\)  points, as even storing a single point requires \(\Omega (d)\)  space. In particular, the \(d\) -dimensional representation of the coreset points is never stored. Even though [1]} does not explicitly mention this in Corollary 5.18, it can be verified by inspecting Algorithm 1. One additional fact is needed in Step 2 of Algorithm 1 of [1]}: a \(O(1)\) -approximate center set \(C^*\)  may be found using a subset of the dataset points when \(z \ge 1\)  is not too large.
